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In this paper, we present data from the Blind Ultra-Deep HI Environmental Survey (BUDHIES), which is a blind 21-cm HI spectral line imaging survey undertaken with the Westerbork Synthesis Radio Telescope (WSRT). Two volumes were surveyed, each with a single pointing and covering a redshift range of 0.164 < z < 0.224. Within these two volumes, this survey targeted the clusters Abell 963 and Abell 2192, which are dynamically different and offer unique environments to study the process of galaxy evolution within clusters. With an integration time of 117x12h on Abell 963 and 72x12h on Abell 2192, a total of 166 galaxies were detected and imaged in HI. While the clusters themselves occupy only 4 per cent of the 73,400 Mpc$^3$ surveyed by BUDHIES, most of the volume consists of large-scale structures in which the clusters are embedded, including foreground and background overdensities and voids. We present the data processing and source detection techniques and counterpart identification based on a wide-field optical imaging survey using the Isaac Newton Telescope (INT) and deep ultra-violet GALEX imaging. Finally, we present HI and optical catalogues of the detected sources as well as atlases of their global HI properties, which include integrated column density maps, position-velocity diagrams, global HI profiles, and optical and UV images of the HI sources.